Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
class CodeforcesTask815ASolution:
    def __init__(self):
        self.result = ''
        self.n_m = []
        self.board = []

    def read_input(self):
        self.n_m = [int(x) for x in input().split(" ")]
        for x in range(self.n_m[0]):
            self.board.append([int(y) for y in input().split(" ")])

    def process_task(self):
        columns = []
        for x in range(self.n_m[1]):
            column = []
            for y in range(self.n_m[0]):
                column.append(self.board[y][x])
            columns.append(column)

        left_board_moves = [min(row) for row in self.board]
        bottom_board_moves = [min(column) for column in columns]
        reduce1 = min(bottom_board_moves)
        reduce2 = min(left_board_moves)
        if reduce1 * self.n_m[0] > reduce2 * self.n_m[1]:
            left_board_moves = [x - reduce1 for x in left_board_moves]
        else:
            bottom_board_moves = [x - reduce2 for x in bottom_board_moves]
        moves = sum(left_board_moves) + sum(bottom_board_moves)
        board_score = sum(left_board_moves) * self.n_m[1] + sum(bottom_board_moves) * self.n_m[0]
        real_board_score = sum([sum(x) for x in self.board])
        if board_score != real_board_score:
            self.result = "-1"
        else:
            print("{0}".format(moves))
            for x in range(self.n_m[0]):
                for y in range(left_board_moves[x]):
                    print("row {0}".format(x + 1))
            for x in range(self.n_m[1]):
                for y in range(bottom_board_moves[x]):
                    print("col {0}".format(x + 1))

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask815ASolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())